Existence of Solutions for Steady Detonation of Gas Suspensions

The existence of solutions of the traveling–wave type is studied for a system of equations that describes a one–dimensional motion of a suspension of evaporating particles in a viscous and heat–conducting chemically reacting gas. Using topological methods, it is shown that solutions corresponding to weak, strong, and Chapman—Jouguet detonation exist under certain restrictions on energy release and mass transfer.     

NUMERICAL SOLUTIONS OF ONE–DIMENSIONAL MHD EQUATIONS BY A FLUCTUATION APPROACH

In this paper a higher-order Godunov method for one-dimensional solutions of the ideal MHD (magneto-hydrodynamics) equations is presented. The method uses a fluctuation approach and includes a new sonic fix and a new Roe averaging. After a short introduction the MHD equations in conservative form are given. The flux is rearranged such that the eigenstructure is not changed. This rearrangement allows full Roe averaging for any value of adiabatic index (contrary to Brio and Wu's conclusion). A new procedure to get Roe—averaged MHD fields at the interfaces between left and right states is then presented and some useful identities are given. Next the second-order-limited fluctuation approach is presented in full detail. The new sonic fix for MHD and the procedure for applying this fix to the sonic points are then given in detail. Numerical results obtained with the described method are presented. Finally, conclusions are given.     

Detonation in heterogeneous mixtures of liquids and particles

The mechanisms of detonation propagation in heterogeneous systems comprising closely packed particles and a liquid explosive are not fully understood. Recent experimental work has suggested the presence of two distinct modes of detonation propagation. One mode is valid for small particles (which is the regime we will address in this paper) with another mode for large particles. In this work we model numerically the detail of the wave interactions between the detonating liquid and the solid particles. The generic system of interest in our work is nitromethane and aluminium but our methodology can be applied to other liquids and particles. We have exercised our numerical models on the experiments described above. Our models can now qualitatively explain the observed variation in critical diameter with particle size. We also report some initial discrepancies in our predictions of wave speeds in nominally one dimensional experiments which can be explained by detailed modelling. We find that the complex wave interaction in the flow behind the leading shock in the detonating system of liquid and particles is characterised by at least two sonic points. The first is the standard CJ point in the reacting liquid. The second is a sonic point with respect to the sound speed in the inert material. This leads to a steady state zone in the flow behind the leading shock which is much longer than the reaction zone in the liquid alone. The width of this region scales linearly with particle size. Since the width of the subsonic region strongly influences the failure diameter we believe that this property of the flow is the origin of the observed increase in failure diameter with particle size for small inert particles. Received 3 December 1999 / Accepted 5 July 2000     

Kinetic Stabilization¶of a Nonlinear Sonic Phase Boundary

We consider a system arising in the study of phase transitions in elastodynamics – a system of two conservation laws, in a single space dimension. The system has two hyperbolic regions with an elliptic zone in between. A phase boundary is a strong discontinuity in a solution, with left and right states belonging to different hyperbolic regions. We call such a solution a phase wave. We first address the Riemann problem for initial states close to a fixed sonic phase wave, in the genuinely nonlinear case. This problem is naturally underdetermined. We propose two essentially different types of Reimann problems: a sonic one, which is smooth, and a kinetic one, which is only Lipschitz-continuous. Both problems are well posed owing to a shared stability condition that is of a purely sonic nature. In the kinetic case we prove the global existence of solutions to the Cauchy problem for initial data having small variation and close to a sonic kinetic wave. The crucial issue is the interaction of the phase boundary with a small wave of the same mode. The introduction of a pertinent quantity, called here detonation potential, ensures a balance between ingoing and outgoing waves. The proof is based on a Glimm-type scheme; we define a potential, which includes the detonation potential, along the strong discontinuity, and this potential controls the outbreak of unusual shocks. Accepted: June 9, 1999     

The Osher scheme for non-equilibrium reacting flows

An extension of the Osher upwind scheme to non-equilibrium reacting flows is presented, Owing to the presence of source terms, the Riemann problem is no longer self-similar and therefore its approximate solution becomes tedious. With simplicity in mind, a linearized approach which avoids an iterative solution is used to define the intermediate states and sonic points. The source terms are treated explicitly. Numerical computations are presented to demonstrate the feasibility, efficiency and accuracy of the proposed method. The test problems include a ZND (Zeldovich-Neumann-Doring) detonation problem for which spurious numerical solutions which propagate at mesh speed have been observed on coarse grids. With the present method, a change of limiter causes the solution to change from the physically correct CJ detonation solution to the spurious weak detonation solution.     

Head-on Collision of a Detonation with a Planar Shock Wave

The phenomenon that occurs when a Chapman–Jouguet (CJ) detonation collides with a shock wave is discussed. Assuming a one-dimensional steady wave configuration analogous to a planar shock–shock frontal interaction, analytical solutions of the Rankine–Hugoniot relationships for the transmitted detonation and the transmitted shock are obtained by matching the pressure and particle velocity at the contact surface. The analytical results indicate that there exist three possible regions of solutions, i.e. the transmitted detonation can have either strong, weak or CJ solution, depending on the incident detonation and shock strengths. On the other hand, if we impose the transmitted detonation to have a CJ solution followed by a rarefaction fan, the boundary conditions are also satisfied at the contact surface. The existence of these multiple solutions is verified by an experimental investigation. It is found that the experimental results agree well with those predicted by the second wave interaction model and that the transmitted detonation is a CJ detonation. Unsteady numerical simulations of the reactive Euler equations with both simple one-step Arrhenius kinetic and chain-branching kinetic models are also carried out to look at the transient phenomena and at the influence of a finite reaction thickness of a detonation wave on the problem of head-on collision with a shock. From all the computational results, a relaxation process consisting of a quasi-steady period and an overshoot for the transmitted detonation subsequent to the head-on collisions can be observed, followed by the asymptotic decay to a CJ detonation as predicted theoretically. For unstable pulsating detonations, it is found that, due to the increase in the thermodynamic state of the reactive mixture caused by the shock, the transmitted pulsating detonation can become more stable with smaller amplitude and period oscillation. These observations are in good agreement with experimental evidence obtained from smoked foils where there is a significant decrease in the detonation cell size after a region of relaxation when the detonation collides head-on with a shock wave.     

2021-08期封面

铝粉反应模型是对悬浮铝粉尘气-固两相爆轰进行数值模拟研究的关键。通过考虑铝粉燃烧产物氧化铝（Al₂O₃）在高温下的分解吸热反应,改进了铝粉的扩散燃烧模型。将该模型嵌入到三维的气-固两相爆轰数值计算程序中,分别对铝粉/空气混合物以及铝粉/氧气混合物的爆轰进行了数值模拟,计算得到的稳定爆轰波速度与实验结果、文献值均吻合较好,误差小于5.5%,表明改进的铝粉反应模型适用于不同氧化气体氛围中铝粉尘爆轰的模拟计算。此外,对两相爆轰参数及爆轰流场的物理量分布进行分析,获得了铝粉反应模型对爆轰波结构的影响规律。     

A class of exact solutions of the ideal plasticity equations

A class of exact solutions is formulated for the ideal plasticity equations in the case of plane deformation. The solutions describe the plastic state of various wedges, notched half-planes, and domains in the form of funnels produced by detonation, the plastic state of domains having a horn configuration, etc. Many of the solutions have natural boundaries comprising envelopes of slip lines. The equations for the boundaries, slip lines, and stresses are presented in explicit form.     

爆轰等容终点的四组理论解

用Hamilton原理描述爆轰产物粒子运动并最终耗散为热的过程,证明爆轰过程反应区有四组理论解可以达到等容终点,即反应区的多变量解、等温过程解、等压过程解、等容过程解;修正了经典的ZND模型由于忽略输运效应而认为爆轰过程不可能达到等容终点的结论。本文结果与实验结果较为一致。     

Steady detonation waves for gases undergoing dissociation/recombination and bimolecular reactions

The one-dimensional steady propagation problem of a shock wave that models detonation as a combustion process in a mixture of reacting gases is studied. For this purpose, suitable reactive Euler equations deduced from appropriate closures of the Boltzmann-like equations holding at the mesoscopic level are used. The considered chemical reactions driving detonation are of either the dissociation/recombination or bimolecular type. After a jump discontinuity governed by the Rankine-Hugoniot conditions, the reactions proceed until chemical equilibrium is reached. The physical consistency of the solutions is discussed in terms of the relevant Hugoniot diagrams, which show different features for exothermic and endothermic processes and determine the allowed range of detonation velocities.Received: 22 January 2003, Accepted: 28 June 2003PACS: 47.40.-x, 82.40.-g, 47.70.Fw Correspondence to: R. Monaco     

Intensification of a detonation wave in the zone of secondary reactions in a two-phase medium

A method is proposed for the numerical calculation of one-dimensional nonsteady-state flows of a mixture of a gas with particles, based on the separation of a system of differential equations for a two-phase medium into two subsystems. The problem is solved concerning the propagation of a plane detonation wave in a mixture of a detonating gas with particles, behind the front of which secondary chemical reactions are taking place between the vapors of the particle material and the detonation products. The velocity profiles of the gas and of the thermodynamic functions behind the detonation wave front are determined, and also the dependence of the detonation velocity on the distance to the point of initiation. The conditions for intensification of the detonation wave are obtained in the zone of secondary reactions.Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 92–96, September–October, 1972.     

A Geometrical Approach to Nonconservative Shocks and Elastoplastic Shocks

We study systems of conservation laws with convex inequality constraints. We analyze shock solutions for the underlying nonconservative system of partial differential equations. Then we study a model elastoplastic system of partial differential equations in the context of hypoelasticity. We show that a sonic point is necessary to construct a compression solution that begins at a constrained compressed state.     

Numerical predictions of oblique detonation stability boundaries

Oblique detonation stability was studied by numerically integrating the two-dimensional, one-step reactive Euler equations in a generalized, curvilinear coordinate system. The integration was accomplished using the Roe scheme combined with fractional stepping; nonlinear flux limiting was used to prevent unphysical solution oscillations near discontinuities. The method was verified on one- and two-dimensional flows with exact solutions, and its ability to correctly predict one-dimensional detonation stability boundaries was demonstrated. The behavior of straight oblique detonations attached to curved walls was then considered. Using the exact, steady oblique detonation solution as an initial condition, the numerical simulation predicted both steady and unsteady oblique detonation solutions when a detonation parameter known as the normal overdrive, , was varied. For a standard test case with a specific heat ratio of , a dimensionless activation energy of , and dimensionless heat release of , an oblique detonation with a constant dimensionless component of velocity tangent to the lead shock, , underwent transition to unstable behavior at . This is slightly higher than the threshold of predicted by one-dimensional theory; thus, the two-dimensionality renders the flow slightly more susceptible to instability. Received 4 August 1996 / Accepted 5 March 1996     

Investigation of the detonation regimes in gaseous mixtures with suspended starch particles

The existence of a secondary discontinuity at the rear of a detonation front shown in experiments by Peraldi and Veyssiere (1986) in stoichiometric hydrogen-oxygen mixtures with suspended 20-m starch particles has not been explained satisfactorily. Recently Veyssiere et al. (1997) analyzed these results using a one-dimensional (1-D) numerical model, and concluded that the heat release rate provided by the burning of starch particles in gaseous detonation products is too weak to support a double-front detonation (DFD), in contrast to the case of hybrid mixtures of hydrogen-air with suspended aluminium particles in which a double-front detonation structure was observed by Veyssiere (1986). A two-dimensional (2-D) numerical model was used in the present work to investigate abovementioned experimental results for hybrid mixtures with starch particles. The formation and propagation of the detonation has been examined in the geometry similar to the experimental tube of Peraldi and Veyssiere (1986), which has an area change after 2 m of propagation from the ignition point from a 69 mm dia. section to a 53 mm 53 mm square cross section corresponding to a 33% area contraction. It is shown that the detonation propagation regime in these experiments has a different nature from the double-front detonation observed in hybrid mixtures with aluminium particles. The detonation propagates as a pseudo-gas detonation (PGD) because starch particles release their heat downstream of the CJ plane giving rise to a non-stationary compression wave. The discontinuity wave at the rear of the detonation front is due to the interaction of the leading detonation front with the tube contraction, and is detected at the farthest pressure gauge location because the tube length is insufficient for the perturbation generated by the tube contraction to decay. Thus, numerical simulations explain experimental observations made by Peraldi and Veyssiere (1986). Received 5 July 1997 / Accepted 13 July 1998     

惰性颗粒抑爆过程的数值模拟

对高温火球诱导的爆炸及惰性颗粒的抑爆过程进行了数值研究。由于扰动特征时间 ,两相弛豫特征时间和化学平衡特征时间的差异 ,这种带激波的两相化学反应流守恒方程具有刚性。利用处理包括组元守恒方程的全耦合TVD格式和可处理方程源项的Lax Wendroff Rubin格式分别求解气相和颗粒相 ,并根据各特征时间的比值用分步法处理方程的刚性。计算结果反映了均温燃烧火球在可燃环境中形成加速火焰和激波 ,进而成长为爆轰波的过程 ,以及惰性颗粒对爆轰波的抑制过程 ,反映了激波、化学反应和惰性颗粒之间的相互作用和耦合。计算结果表明 ,仅当颗粒浓度大于某值时才能有效抑制爆轰 ,否则无论多大的颗粒散布区域 ,皆不能使爆轰波完全抑制 ,爆轰波或是在其中发展为两相爆轰波 ,或是穿越该区域后重新成长为气相爆轰。     

Semi-hyperbolic Patches of Solutions to the Two-dimensional Euler Equations

We construct semi-hyperbolic patches of solutions, in which one family out of two nonlinear families of characteristics starts on sonic curves and ends on transonic shock waves, to the two-dimensional Euler equations. This type of solution appears in the transonic flow over an airfoil and Guderley reflection, and is common in the numerical solutions of Riemann problems.     

Dynamic characteristics of spherically converging detonation waves

The spherically converging detonation wave was numerically investigated by solving the one-dimensional multi-component Euler equations in spherical coordinates with a dispersion-controlled dissipative scheme. Finite rate and detailed chemical reaction models were used and numerical solutions were obtained for both a spherical by converging detonation in a stoichiometric hydrogen-oxygen mixture and a spherically focusing shock in air. The results showed that the post-shock pressure approximately arises to the same amplitude in vicinity of the focal point for the two cases, but the post-shock temperature level mainly depends on chemical reactions and molecular dissociations of a gas mixture. While the chemical reaction heat plays an important role in the early stage of detonation wave propagation, gas dissociations dramatically affect the post-shock flow states near the focal point. The maximum pressure and temperature, non-dimensionalized by their initial value, are approximately scaled to the propagation radius over the initial detonation diameter. The post-shock pressure is proportional to the initial pressure of the detonable mixture, and the post-shock temperature is also increased with the initial pressure, but in a much lower rate than that of the post-shock pressure. Zonglin Jiang is presently a visiting professor at McGill University, Canada.     

Rapid detonation initiation by sparks in a short duct: a numerical study

Rapid onset of detonation can efficiently increase the working frequency of a pulse detonation engine (PDE). In the present study, computations of detonation initiation in a duct are conducted to investigate the mechanisms of detonation initiation. The governing equations are the Euler equations and the chemical kinetic model consists of 19 elementary reactions and nine species. Different techniques of initiation have been studied for the purpose of accelerating detonation onset with a relatively weak ignition energy. It is found that detonation ignition induced by means of multiple sparks is applicable to auto-ignition for a PDE. The interaction among shock waves, flame fronts and the strip of pre-compressed fresh (unburned) mixture plays an important role in rapid onset of detonation.